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Diagonal Lemma

  1. Nov 16, 2013 #1


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    The diagonal lemma (which can be used to prove the Gödel-Tarski Theorem, among others) apparently goes, in a nutshell,

    suppose you have a one-place formula A(.) with domain the set of codes of sentences.
    I use quotation marks in this way : "M" is the code of M.
    Define the 2-place relation sub:
    If x ="f(.)", then sub(x,x) = "f(x)"
    Define B(x) as A(sub (x,x))
    Define S as B("B(x)")
    retracing, S is true iff A("S") is.

    Nice. What I do not understand is that the proof notes that S and A("S") are equivalent but not the same. It appears to me from the construction that they are the same. What am I missing?
  2. jcsd
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